Conventionally, there is known, as an exhaust purification system for an internal combustion engine, an exhaust purification system including a NOx catalyst for reducing and purifying nitrogen oxides (hereinafter, referred to as NOx) in exhaust gas and an oxidation catalyst. NOx catalysts and oxidation catalysts cannot exhibit sufficiently their purification performances unless their catalyst temperatures reach or exceed their activation temperatures. Due to this, in a situation where the temperature of exhaust gas lowers as when a vehicle is being decelerated, a so-called catalyst temperature retention control is preferably executed in which the temperature of a catalyst is retained by suppressing effectively the flow of exhaust gas of a low temperature into the catalyst by reducing an intake air flow (an exhaust gas flow) (for example, refer to Patent Literatures 1, 2).